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Countably compact and pseudocompact topologies on free Abelian groups. (English. Russian original) Zbl 0714.22001
Sov. Math. 34, No. 5, 79-86 (1990); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1990, No. 5(336), 68-75 (1990).
It is well known that any non-trivial free Abelian group does not admit a compact Hausdorff group topology. In connection with this result the author proves the following results: Theorem 1 (CH). On the free Abelian group G of cardinality \(c=2^{\aleph_ 0}\) there exists a countably compact Hausdorff group topology \({\mathcal T}\) such that the group \(<G,{\mathcal T}>\) is connected, locally connected, hereditarily separable and hereditarily normal. Theorem 2. On the free Abelian group of cardinality \(2^{\aleph_ 0}\) there exists a chain \({\mathfrak A}\) of pseudocompact Hausdorff group topologies such that \(| {\mathfrak A}| =2^{(c^+)}\), where \(c^+\) is the smallest cardinal larger than c.
Reviewer: M.I.Ursul

22A05 Structure of general topological groups
20K45 Topological methods for abelian groups
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
20K20 Torsion-free groups, infinite rank